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%I #19 Jun 26 2018 07:47:44
%S 1,1,2,2,4,5,7,8,12,14,20,23,31,37,47,56,71,84,104,122,151,178,215,
%T 252,303,355,423,492,582,676,795,920,1076,1242,1445,1662,1926,2210,
%U 2549,2916,3353,3827,4386,4992,5703,6478,7379,8362,9499,10742,12174,13738,15533,17496,19736,22190,24979
%N McKay-Thompson series of class 42d for Monster.
%H G. C. Greubel, <a href="/A058678/b058678.txt">Table of n, a(n) for n = -1..1000</a>
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of q^(1/2)*(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) in powers of q. - _G. C. Greubel_, Jun 26 2018
%F a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018
%e T42d = 1/q + q + 2*q^3 + 2*q^5 + 4*q^7 + 5*q^9 + 7*q^11 + 8*q^13 + 12*q^15 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q^(1/2)*(eta[q^3]*eta[q^7]/(eta[q]*eta[q^21])), {q, 0, 60}], q]; Table[a[n], {n, 0, 50}] (* _G. C. Greubel_, Jun 26 2018 *)
%o (PARI) q='q+O('q^60); Vec(eta(q^3)*eta(q^7)/(eta(q)*eta(q^21))) \\ _G. C. Greubel_, Jun 26 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K nonn
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000
%E Terms a(12) onward added by _G. C. Greubel_, Jun 26 2018
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